%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL573+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:13:04 PM UTC 2026
% Result : Theorem 3.30s 1.20s
% Output : CNFRefutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 30
% Syntax : Number of formulae : 154 ( 86 unt; 0 def)
% Number of atoms : 277 ( 59 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 211 ( 88 ~; 88 |; 17 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 19 con; 0-2 aty)
% Number of variables : 228 ( 17 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X2)
& is_a_theorem(X1) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X1,X2] : strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X1,X2] :
( is_a_theorem(strict_equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
fof(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_substitution_strict_equiv) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X2] :
( ( is_a_theorem(strict_implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(axiom_m5,axiom,
( axiom_m5
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m5) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_modus_ponens_strict_implies) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_implies) ).
fof(s1_0_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_or) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m2) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m4) ).
fof(axiom_m3,axiom,
( axiom_m3
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m3) ).
fof(s1_0_axiom_m3,axiom,
axiom_m3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m3) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X1] : possibly(X1) = not(necessarily(not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(s1_0_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_possibly) ).
fof(axiom_m10,axiom,
( axiom_m10
<=> ! [X1] : is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m10) ).
fof(km5_axiom_5,conjecture,
axiom_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(s1_0_m10_axiom_m10,axiom,
axiom_m10,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+6.ax',s1_0_m10_axiom_m10) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X1] : is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
fof(c_0_30,plain,
! [X22,X23] :
( ( adjunction
| ~ is_a_theorem(and(esk4_0,esk5_0)) )
& ( adjunction
| is_a_theorem(esk5_0) )
& ( adjunction
| is_a_theorem(esk4_0) )
& ( is_a_theorem(and(X22,X23))
| ~ is_a_theorem(X23)
| ~ is_a_theorem(X22)
| ~ adjunction ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])])]) ).
fof(c_0_31,plain,
! [X98,X99] :
( strict_equiv(X98,X99) = and(strict_implies(X98,X99),strict_implies(X99,X98))
| ~ op_strict_equiv ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])])]) ).
fof(c_0_32,plain,
! [X26,X27] :
( ( substitution_strict_equiv
| esk6_0 != esk7_0 )
& ( substitution_strict_equiv
| is_a_theorem(strict_equiv(esk6_0,esk7_0)) )
& ( X26 = X27
| ~ is_a_theorem(strict_equiv(X26,X27))
| ~ substitution_strict_equiv ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_strict_equiv])])])])])]) ).
cnf(c_0_33,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ adjunction
| is_a_theorem(and(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
cnf(c_0_35,plain,
( ~ op_strict_equiv
| strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
cnf(c_0_37,plain,
( ~ is_a_theorem(strict_equiv(X1,X2))
| ~ substitution_strict_equiv
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_39,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X2)
| is_a_theorem(and(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_40,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
fof(c_0_41,plain,
! [X58,X59] :
( ( axiom_m1
| ~ is_a_theorem(strict_implies(and(esk22_0,esk23_0),and(esk23_0,esk22_0))) )
& ( is_a_theorem(strict_implies(and(X58,X59),and(X59,X58)))
| ~ axiom_m1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])])]) ).
fof(c_0_42,plain,
! [X18,X19] :
( ( modus_ponens_strict_implies
| ~ is_a_theorem(esk3_0) )
& ( modus_ponens_strict_implies
| is_a_theorem(strict_implies(esk2_0,esk3_0)) )
& ( modus_ponens_strict_implies
| is_a_theorem(esk2_0) )
& ( is_a_theorem(X19)
| ~ is_a_theorem(strict_implies(X18,X19))
| ~ is_a_theorem(X18)
| ~ modus_ponens_strict_implies ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens_strict_implies])])])])])]) ).
fof(c_0_43,plain,
! [X74,X75,X76] :
( ( axiom_m5
| ~ is_a_theorem(strict_implies(and(strict_implies(esk30_0,esk31_0),strict_implies(esk31_0,esk32_0)),strict_implies(esk30_0,esk32_0))) )
& ( is_a_theorem(strict_implies(and(strict_implies(X74,X75),strict_implies(X75,X76)),strict_implies(X74,X76)))
| ~ axiom_m5 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])])]) ).
fof(c_0_44,plain,
! [X10,X11] :
( implies(X10,X11) = not(and(X10,not(X11)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
cnf(c_0_45,plain,
( ~ is_a_theorem(strict_equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_46,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(strict_equiv(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
( ~ axiom_m1
| is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
cnf(c_0_49,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_51,plain,
( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
fof(c_0_53,plain,
! [X96,X97] :
( strict_implies(X96,X97) = necessarily(implies(X96,X97))
| ~ op_strict_implies ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])]) ).
fof(c_0_54,plain,
! [X6,X7] :
( or(X6,X7) = not(and(not(X6),not(X7)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_55,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_57,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_60,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
fof(c_0_61,plain,
! [X62,X63] :
( ( axiom_m2
| ~ is_a_theorem(strict_implies(and(esk24_0,esk25_0),esk24_0)) )
& ( is_a_theorem(strict_implies(and(X62,X63),X62))
| ~ axiom_m2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])])]) ).
cnf(c_0_62,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_64,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
cnf(c_0_66,plain,
op_or,
inference(split_conjunct,[status(thm)],[s1_0_op_or]) ).
cnf(c_0_67,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_58])]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
( ~ axiom_m2
| is_a_theorem(strict_implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_71,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_72,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
cnf(c_0_73,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_67]) ).
fof(c_0_74,plain,
! [X72] :
( ( axiom_m4
| ~ is_a_theorem(strict_implies(esk29_0,and(esk29_0,esk29_0))) )
& ( is_a_theorem(strict_implies(X72,and(X72,X72)))
| ~ axiom_m4 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])])]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(strict_implies(X1,X3))
| ~ is_a_theorem(strict_implies(X3,X2))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_68,c_0_39]) ).
cnf(c_0_76,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_77,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_73]),c_0_72]),c_0_72]) ).
cnf(c_0_79,plain,
( ~ axiom_m4
| is_a_theorem(strict_implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_81,plain,
( ~ is_a_theorem(strict_implies(X1,and(X2,X3)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_77]) ).
cnf(c_0_83,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(strict_implies(not(and(X2,X3)),X1))
| is_a_theorem(strict_implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_83]),c_0_76])]) ).
cnf(c_0_86,plain,
is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_83]),c_0_85]),c_0_82]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(strict_implies(X1,not(X3)))
| ~ is_a_theorem(strict_implies(not(X2),X3))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_82]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(strict_implies(not(X2),X1))
| is_a_theorem(strict_implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,plain,
is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_86,c_0_73]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(strict_implies(X1,not(X2)))
| ~ is_a_theorem(strict_implies(not(X1),X2))
| X1 = not(X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_82]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(strict_implies(X1,not(not(X2))))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_83]),c_0_85]) ).
cnf(c_0_92,plain,
is_a_theorem(strict_implies(not(implies(X1,X2)),not(X2))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(strict_implies(X1,not(not(X1))))
| not(not(X1)) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_83]),c_0_85]),c_0_85]) ).
cnf(c_0_94,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_85]),c_0_72]) ).
cnf(c_0_95,plain,
is_a_theorem(strict_implies(not(X1),implies(X2,not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_82]) ).
fof(c_0_96,plain,
! [X66,X67,X68] :
( ( axiom_m3
| ~ is_a_theorem(strict_implies(and(and(esk26_0,esk27_0),esk28_0),and(esk26_0,and(esk27_0,esk28_0)))) )
& ( is_a_theorem(strict_implies(and(and(X66,X67),X68),and(X66,and(X67,X68))))
| ~ axiom_m3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m3])])])])]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(strict_implies(X1,or(X1,X1)))
| or(X1,X1) = X1 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,plain,
is_a_theorem(strict_implies(not(X1),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_95,c_0_72]) ).
cnf(c_0_99,plain,
( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_100,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_101,plain,
not(not(not(X1))) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_94]) ).
cnf(c_0_102,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100])]) ).
cnf(c_0_103,plain,
implies(X1,not(not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_101]),c_0_73]) ).
cnf(c_0_104,plain,
( ~ is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))
| and(and(X1,X2),X3) = and(X1,and(X2,X3)) ),
inference(spm,[status(thm)],[c_0_57,c_0_102]) ).
cnf(c_0_105,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_76,c_0_67]) ).
cnf(c_0_106,plain,
strict_implies(X1,not(not(X2))) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_103]),c_0_71]) ).
cnf(c_0_107,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_76,c_0_85]) ).
cnf(c_0_108,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_85]),c_0_105])]) ).
cnf(c_0_109,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_106]),c_0_107])]) ).
cnf(c_0_110,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_108,c_0_67]) ).
cnf(c_0_111,plain,
not(implies(X1,X2)) = and(not(X2),X1),
inference(spm,[status(thm)],[c_0_109,c_0_73]) ).
cnf(c_0_112,plain,
implies(and(X1,not(X2)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_110]),c_0_65]) ).
cnf(c_0_113,plain,
and(not(X1),not(X2)) = not(or(X2,X1)),
inference(spm,[status(thm)],[c_0_111,c_0_72]) ).
cnf(c_0_114,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_109]) ).
cnf(c_0_115,plain,
or(X1,or(X1,X2)) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_72]),c_0_72]),c_0_78]) ).
cnf(c_0_116,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_78,c_0_114]) ).
cnf(c_0_117,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_86,c_0_65]) ).
cnf(c_0_118,plain,
necessarily(not(not(X1))) = strict_implies(not(X1),X1),
inference(spm,[status(thm)],[c_0_77,c_0_94]) ).
cnf(c_0_119,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]),c_0_114]) ).
fof(c_0_120,plain,
! [X94] :
( possibly(X94) = not(necessarily(not(X94)))
| ~ op_possibly ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])]) ).
cnf(c_0_121,plain,
strict_implies(not(X1),not(X2)) = strict_implies(X2,X1),
inference(spm,[status(thm)],[c_0_82,c_0_109]) ).
cnf(c_0_122,plain,
( ~ is_a_theorem(strict_implies(X1,not(X2)))
| is_a_theorem(strict_implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_75,c_0_117]) ).
cnf(c_0_123,plain,
strict_implies(not(X1),X1) = necessarily(X1),
inference(rw,[status(thm)],[c_0_118,c_0_109]) ).
cnf(c_0_124,plain,
strict_implies(X1,implies(X1,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_119]),c_0_71]) ).
cnf(c_0_125,plain,
( ~ op_possibly
| possibly(X1) = not(necessarily(not(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_126,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[s1_0_op_possibly]) ).
cnf(c_0_127,plain,
strict_implies(X1,not(X2)) = strict_implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_121,c_0_109]) ).
cnf(c_0_128,plain,
( ~ is_a_theorem(necessarily(not(X1)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_109]),c_0_124]) ).
fof(c_0_129,plain,
! [X92] :
( ( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(esk39_0),necessarily(possibly(esk39_0)))) )
& ( is_a_theorem(strict_implies(possibly(X92),necessarily(possibly(X92))))
| ~ axiom_m10 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m10])])])])]) ).
cnf(c_0_130,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126])]) ).
fof(c_0_131,negated_conjecture,
~ axiom_5,
inference(assume_negation,[status(cth)],[km5_axiom_5]) ).
cnf(c_0_132,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X1,not(X2)))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_59,c_0_127]) ).
cnf(c_0_133,plain,
( ~ is_a_theorem(necessarily(X1))
| is_a_theorem(strict_implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_128,c_0_109]) ).
cnf(c_0_134,plain,
( ~ axiom_m10
| is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_135,plain,
axiom_m10,
inference(split_conjunct,[status(thm)],[s1_0_m10_axiom_m10]) ).
cnf(c_0_136,plain,
not(and(X1,possibly(X2))) = implies(X1,necessarily(not(X2))),
inference(spm,[status(thm)],[c_0_65,c_0_130]) ).
fof(c_0_137,negated_conjecture,
~ axiom_5,
inference(fof_simplification,[status(thm)],[c_0_131]) ).
cnf(c_0_138,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_109]) ).
cnf(c_0_139,plain,
is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]) ).
cnf(c_0_140,plain,
possibly(and(X1,not(X2))) = not(strict_implies(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_65]),c_0_71]) ).
cnf(c_0_141,plain,
or(X1,necessarily(not(X2))) = implies(possibly(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_73]),c_0_72]) ).
fof(c_0_142,plain,
! [X40] :
( ( axiom_5
| ~ is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0)))) )
& ( is_a_theorem(implies(possibly(X40),necessarily(possibly(X40))))
| ~ axiom_5 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])])]) ).
fof(c_0_143,negated_conjecture,
~ axiom_5,
inference(fof_nnf,[status(thm)],[c_0_137]) ).
cnf(c_0_144,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(strict_implies(X1,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_138,c_0_71]) ).
cnf(c_0_145,plain,
is_a_theorem(strict_implies(not(strict_implies(X1,X2)),necessarily(not(strict_implies(X1,X2))))),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_146,plain,
strict_implies(not(X1),necessarily(not(X2))) = strict_implies(possibly(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_141]),c_0_71]) ).
cnf(c_0_147,plain,
( ~ is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0))))
| axiom_5 ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_148,negated_conjecture,
~ axiom_5,
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_149,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))) ),
inference(spm,[status(thm)],[c_0_144,c_0_139]) ).
cnf(c_0_150,plain,
is_a_theorem(strict_implies(possibly(strict_implies(X1,X2)),strict_implies(X1,X2))),
inference(rw,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_151,plain,
~ is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0)))),
inference(sr,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_152,plain,
is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_153,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_152])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL573+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.51 % Computer : n004.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Mon Sep 21 00:39:51 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.56 Running first-order theorem proving
% 0.16/0.56 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.30/1.20 % Version: 3.5.1
% 3.30/1.20 % Preprocessing class: FSMSSLSSSSSNFFN.
% 3.30/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.30/1.20 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 3.30/1.20 % Starting new_bool_3 with 300s (1) cores
% 3.30/1.20 % Starting new_bool_1 with 300s (1) cores
% 3.30/1.20 % Starting sh5l with 300s (1) cores
% 3.30/1.20 % new_bool_3 with pid 1887429 completed with status 9
% 3.30/1.20 % new_bool_1 with pid 1887430 completed with status 9
% 3.30/1.20 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1887428 completed with status 0
% 3.30/1.20 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 3.30/1.20 % Preprocessing class: FSMSSLSSSSSNFFN.
% 3.30/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.30/1.20 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 3.30/1.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.30/1.20 % No SInE strategy applied
% 3.30/1.20 % Search class: FGUSF-FFMM21-MFFFFFNN
% 3.30/1.20 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.30/1.20 % Starting SubtermCWHack with 151s (1) cores
% 3.30/1.20 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 3.30/1.20 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 3.30/1.20 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 3.30/1.20 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.30/1.20 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1887439 completed with status 0
% 3.30/1.20 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 3.30/1.20 % Preprocessing class: FSMSSLSSSSSNFFN.
% 3.30/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.30/1.20 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 3.30/1.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.30/1.20 % No SInE strategy applied
% 3.30/1.20 % Search class: FGUSF-FFMM21-MFFFFFNN
% 3.30/1.20 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.30/1.20 % Starting SubtermCWHack with 151s (1) cores
% 3.30/1.20 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 3.30/1.20 % Preprocessing time : 0.002 s
% 3.30/1.20 % Presaturation interreduction done
% 3.30/1.20
% 3.30/1.20 % Proof found!
% 3.30/1.20 % SZS status Theorem
% 3.30/1.20 % SZS output start CNFRefutation
% See solution above
% 3.30/1.20 % Parsed axioms : 52
% 3.30/1.20 % Removed by relevancy pruning/SinE : 0
% 3.30/1.20 % Initial clauses : 81
% 3.30/1.20 % Removed in clause preprocessing : 0
% 3.30/1.20 % Initial clauses in saturation : 81
% 3.30/1.20 % Processed clauses : 3356
% 3.30/1.20 % ...of these trivial : 232
% 3.30/1.20 % ...subsumed : 2331
% 3.30/1.20 % ...remaining for further processing : 793
% 3.30/1.20 % Other redundant clauses eliminated : 0
% 3.30/1.20 % Clauses deleted for lack of memory : 0
% 3.30/1.20 % Backward-subsumed : 38
% 3.30/1.20 % Backward-rewritten : 127
% 3.30/1.20 % Generated clauses : 23669
% 3.30/1.20 % ...of the previous two non-redundant : 21519
% 3.30/1.20 % ...aggressively subsumed : 0
% 3.30/1.20 % Contextual simplify-reflections : 0
% 3.30/1.20 % Paramodulations : 23669
% 3.30/1.20 % Factorizations : 0
% 3.30/1.20 % NegExts : 0
% 3.30/1.20 % Equation resolutions : 0
% 3.30/1.20 % Disequality decompositions : 0
% 3.30/1.20 % Total rewrite steps : 13892
% 3.30/1.20 % ...of those cached : 11352
% 3.30/1.20 % Propositional unsat checks : 0
% 3.30/1.20 % Propositional check models : 0
% 3.30/1.20 % Propositional check unsatisfiable : 0
% 3.30/1.20 % Propositional clauses : 0
% 3.30/1.20 % Propositional clauses after purity: 0
% 3.30/1.20 % Propositional unsat core size : 0
% 3.30/1.20 % Propositional preprocessing time : 0.000
% 3.30/1.20 % Propositional encoding time : 0.000
% 3.30/1.20 % Propositional solver time : 0.000
% 3.30/1.20 % Success case prop preproc time : 0.000
% 3.30/1.20 % Success case prop encoding time : 0.000
% 3.30/1.20 % Success case prop solver time : 0.000
% 3.30/1.20 % Current number of processed clauses : 564
% 3.30/1.20 % Positive orientable unit clauses : 172
% 3.30/1.20 % Positive unorientable unit clauses: 16
% 3.30/1.20 % Negative unit clauses : 4
% 3.30/1.20 % Non-unit-clauses : 372
% 3.30/1.20 % Current number of unprocessed clauses: 17438
% 3.30/1.20 % ...number of literals in the above : 33961
% 3.30/1.20 % Current number of archived formulas : 0
% 3.30/1.20 % Current number of archived clauses : 229
% 3.30/1.20 % Clause-clause subsumption calls (NU) : 49088
% 3.30/1.20 % Rec. Clause-clause subsumption calls : 43948
% 3.30/1.20 % Non-unit clause-clause subsumptions : 2263
% 3.30/1.20 % Unit Clause-clause subsumption calls : 2574
% 3.30/1.20 % Rewrite failures with RHS unbound : 0
% 3.30/1.20 % BW rewrite match attempts : 524
% 3.30/1.20 % BW rewrite match successes : 153
% 3.30/1.20 % Condensation attempts : 0
% 3.30/1.20 % Condensation successes : 0
% 3.30/1.20 % Termbank termtop insertions : 301872
% 3.30/1.20 % Search garbage collected termcells : 1012
% 3.30/1.20
% 3.30/1.20 % -------------------------------------------------
% 3.30/1.20 % User time : 0.571 s
% 3.30/1.20 % System time : 0.035 s
% 3.30/1.20 % Total time : 0.606 s
% 3.30/1.20 % Maximum resident set size: 3688 pages
% 3.30/1.20
% 3.30/1.20 % -------------------------------------------------
% 3.30/1.20 % User time : 2.836 s
% 3.30/1.20 % System time : 0.207 s
% 3.30/1.20 % Total time : 3.042 s
% 3.30/1.20 % Maximum resident set size: 4608 pages
% 3.30/1.20 % E exiting
%------------------------------------------------------------------------------